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Abstract. In this paper we present an algorithm for effectively computing extremal fixedpoints of a system of mutually recursive equations over a finite transition system. The proposed algorithm runs in time linear in the size of the transition system and linear in the size of the system of equations, thereby improving on [AC].

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This paper presents an algorithm for solving Boolean fixedpoint equations containing one level of nesting of minimum and maximum fixed points. The algorithm assumes that the equations of the inner fixed point is of a certain restricted kind and has a worst-case timeand space-complexity that is linear in the size of the equation system. By observing that a range of behavioral relations-in particular weak bisimulation-and modal assertions can be checked using equation systems of this restricted form, the algorithm improves on existing ad hoc constructed algorithms. Finally, we show how the key idea of inverting a fixed point can be used in decreasing the number of fixed-point iterations needed in BDD-based methods for solving the same class of problems.